# Thread: magic circles?

1. ## magic circles?

Can anyone help me understand how to arrange the digits (odd only) 9-25 in a magic circle so that the sum of the numbers in each straight line is the same? There is one circle inthe middle and 8 around it. There must be a formula to this. Thank you.

2. Hello, gager23!

Arrange the odd numbers from 9 to 25 in a magic circle
so that the sum of the numbers in each straight line is the same.
There is one circle inthe middle and 8 around it.
There really isn't any formula for this, but there is a very logical procedure.

$\text{We have the numbers: }\;9, 11,13,15,\underbrace{17}_{\uparrow},19,21,23,25$
Isn't it reasonable to put the middle number in the center of the circle?

Next, take pairs of numbers "from each end": . $(9,25),\:(11,23),\:(13,21),\:(15,19)$
. .
Note that the pairs have the same sum: 34.

Place the pairs on opposite ends of a diameter.

Then one possible solution looks like this:
Code:
              * 9 *
*     |     *
19       |       11
*  \     |     /  *
\   |   /
*       \ | /       *
21 - - - -17 - - - - 13
*       / | \       *
/   |   \
*  /     |     \  *
23       |       15
*     |     *
*25 *

3. ## magic circle

Thanks for the reply--it makes sense and is appreciated.

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# magic circle math problem with solve

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